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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 128576bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 128576.bw1 | 128576bh1 | \([0, 1, 0, -177, -1009]\) | \(-768208/41\) | \(-32915456\) | \([]\) | \(36864\) | \(0.20138\) | \(\Gamma_0(N)\)-optimal |
| 128576.bw2 | 128576bh2 | \([0, 1, 0, 943, -1681]\) | \(115393712/68921\) | \(-55330881536\) | \([]\) | \(110592\) | \(0.75069\) |
Rank
sage: E.rank()
The elliptic curves in class 128576bh have rank \(1\).
Complex multiplication
The elliptic curves in class 128576bh do not have complex multiplication.Modular form 128576.2.a.bh
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
